Doc, a resistor from collector to emitter on the MJE will cut the power loss considerably. At max output signal if the MJE still conducts 10% to 20% of the idle current, it will still work great. A power resistor is sometimes less expensive than a big (or bigger) heatsink.
If you are concerned about tube arcs, put a diode across base-emitter of the MJE to keep it from avalanching. If you don't care, leave it off and save the nickel.
Note: The LM317 based CCS I've heard sounded very brittle in the highs. I've had slew rate problems with the LM317 at work so I'm blaming the brittleness on the LM317.